Quartic Roots Solver

Polynomial Roots Solver

Port to C++ of the algorithm of Norbert Flocke for polynomial roots up to degree 4. Also Jenkins-Traub real polynomial root finder is ported but is experimental for the moment.

Usage

     #include "PolynomialRoots.hh"

     // ....

     double coeffs[] = { 8, -8, 16,-16, 8,-8 }; // polynomial coeffs

     double zeror[5], zeroi[5];
     int    info[5];
     int    degree = 5;

     int ok = PolynomialRoots::roots( coeffs, degree, zeror, zeroi ); // ok < 0 failed
     cout << " ok = " << ok << '\n' ;
     for ( int i = 0 ; i < degree ; ++i )
       cout << zeror[i] << " + I* " << zeroi[i] << '\n';

To solve quadratic, cubic or quartic use specialized classes

     Quadratic qsolve(a,b,c);
     qsolve.info(cout);

     Cubic csolve(a,b,c,d);
     csolve.info(cout);

     Quartic q4(a,b,c,d,e);
     q4.info(cout);

look at the class definition to see how to access the computed roots.

Repository and Online Documentation

• github
• online doc

References

• N.Flocke
  Algorithm 954: An Accurate and Efficient Cubic and Quartic Equation Solver for Physical Applications
  ACM TOMS, vol 41, n.4, 2015

• M.A. Jenkins and J.F.Traub
  A Three-Stage Algorithm for Real Polynomials Using Quadratic Iteration
  SIAM Journal on Numerical Analysis
  Vol. 7, No. 4 (Dec., 1970), pp. 545-566

Author

Enrico Bertolazzi
Dipartimento di Ingegneria Industriale
Universita` degli Studi di Trento
email: [email protected]